Scattering statistics of rock outcrops: Model-data comparisons and Bayesian inference using mixture distributions

The probability density function of the acoustic field amplitude scattered by the seafloor was measured in a rocky environment off the coast of Norway using a synthetic aperture sonar system, and is reported here in terms of the probability of false alarm. Interpretation of the measurements focused on finding appropriate class of statistical models (single versus two-component mixture models), and on appropriate models within these two classes. It was found that two-component mixture models performed better than single models. The two mixture models that performed the best (and had a basis in the physics of scattering) were a mixture between two K distributions, and a mixture between a Rayleigh and generalized Pareto distribution. Bayes' theorem was used to estimate the probability density function of the mixture model parameters. It was found that the K-K mixture exhibits significant correlation between its parameters. The mixture between the Rayleigh and generalized Pareto distributions also had significant parameter correlation, but also contained multiple modes. We conclude that the mixture between two K distributions is the most applicable to this dataset.Comment: 15 pages, 7 figures, Accepted to the Journal of the Acoustical Society of Americ

Conditional Intensity and Gibbsianness of Determinantal Point Processes

The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a Poisson point process. We also show that determinantal point processes satisfy the so-called condition $(\Sigma_{\lambda})$ which is a general form of Gibbsianness. Under a continuity assumption, the Gibbsian conditional probabilities can be identified explicitly.Comment: revised and extende

Phase Transitions on Nonamenable Graphs

We survey known results about phase transitions in various models of statistical physics when the underlying space is a nonamenable graph. Most attention is devoted to transitive graphs and trees

Electronic Raman scattering in YBCO and other superconducting cuprates

Superconductivity induced structures in the electronic Raman spectra of high-Tc superconductors are computed using the results of ab initio LDA-LMTO three-dimensional band structure calculations via numerical integrations of the mass fluctuations, either in the whole 3D Brillouin zone or limiting the integrations to the Fermi surface. The results of both calculations are rather similar, the Brillouin zone integration yielding additional weak structures related to the extended van Hove singularities. Similar calculations have been performed for the normal state of these high-Tc cuprates. Polarization configurations have been investigated and the results have been compared to experimental spectra. The assumption of a simple d_(x^2-y^2)-like gap function allows us to explain a number of experimental features but is hard to reconcile with the relative positions of the A1g and B1g peaks.Comment: 14 pages, LaTeX (RevTeX), 5 PostScript figures, uses multicol.sty, submitted to PR

Cut Points and Diffusions in Random Environment

In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the discrete setting providing a decoupling effect in the process. This allows us to take advantage of an ergodic structure to derive a strong law of large numbers with possibly vanishing limiting velocity and a central limit theorem under the quenched measure.Comment: 44 pages; accepted for publication in "Journal of Theoretical Probability

Spin Susceptibility and Superexchange Interaction in the Antiferromagnet CuO

Evidence for the quasi one-dimensional (1D) antiferromagnetism of CuO is presented in a framework of Heisenberg model. We have obtained an experimental absolute value of the paramagnetic spin susceptibility of CuO by subtracting the orbital susceptibility separately from the total susceptibility through the $^{63}$Cu NMR shift measurement, and compared directly with the theoretical predictions. The result is best described by a 1D $S=1/2$ antiferromagnetic Heisenberg (AFH) model, supporting the speculation invoked by earlier authors. We also present a semi-quantitative reason why CuO, seemingly of 3D structure, is unexpectedly a quasi 1D antiferromagnet.Comment: 7 pages including 4 tables and 9 figure

A Comparative Gene Map of the Horse (Equus caballus)

A comparative gene map of the horse genome composed of 127 loci was assembled based on the new assignment of 68 equine type I loci and on data published previously. PCR primers based on consensus gene sequences conserved across mammalian species were used to amplify markers for assigning 68 equine type I loci to 27 horse synteny groups established previously with a horse-mouse somatic cell hybrid panel (SCHP, UC Davis). This increased the number of coding genes mapped to the horse genome by over 2-fold and allowed refinements of the comparative mapping data available for this species. In conjunction with 57 previous assignments of type I loci to the horse genome map, these data have allowed us to confirm the assignment of 24 equine synteny groups to their respective chromosomes, to provisionally assign nine synteny groups to chromosomes, and to further refine the genetic composition established with Zoo-FISH of two horse chromosomes. The equine type I markers developed in this study provide an important resource for the future development of the horse linkage and physical genome maps

Anomalous Self-Energy Effects of the B_1g Phonon in Y_{1-x}(Pr,Ca)_xBa_2Cu_3O_7 Films

In Raman spectra of cuprate superconductors the gap shows up both directly, via a redistribution of the electronic background, the so-called "2Delta peaks", and indirectly, e.g. via the renormalization of phononic excitations. We use a model that allows us to study the redistribution and the related phonon self-energy effects simultaneously. We apply this model to the B_1g phonon of Y_{1-x}(Pr,Ca)_xBa_2Cu_3O_7 films, where Pr or Ca substitution enables us to investigate under- and overdoped samples. While various self-energy effects can be explained by the strength and energy of the 2\Delta peaks, anomalies remain. We discuss possible origins of these anomalies.Comment: 6 pages including 4 figure

Mutation, selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure

Proterozoic ocean redox and biogeochemical stasis

The partial pressure of oxygen in Earth’s atmosphere has increased dramatically through time, and this increase is thought to have occurred in two rapid steps at both ends of the Proterozoic Eon (∼2.5–0.543 Ga). However, the trajectory and mechanisms of Earth’s oxygenation are still poorly constrained, and little is known regarding attendant changes in ocean ventilation and seafloor redox. We have a particularly poor understanding of ocean chemistry during the mid-Proterozoic (∼1.8–0.8 Ga). Given the coupling between redox-sensitive trace element cycles and planktonic productivity, various models for mid-Proterozoic ocean chemistry imply different effects on the biogeochemical cycling of major and trace nutrients, with potential ecological constraints on emerging eukaryotic life. Here, we exploit the differing redox behavior of molybdenum and chromium to provide constraints on seafloor redox evolution by coupling a large database of sedimentary metal enrichments to a mass balance model that includes spatially variant metal burial rates. We find that the metal enrichment record implies a Proterozoic deep ocean characterized by pervasive anoxia relative to the Phanerozoic (at least ∼30–40% of modern seafloor area) but a relatively small extent of euxinic (anoxic and sulfidic) seafloor (less than ∼1–10% of modern seafloor area). Our model suggests that the oceanic Mo reservoir is extremely sensitive to perturbations in the extent of sulfidic seafloor and that the record of Mo and chromium enrichments through time is consistent with the possibility of a Mo–N colimited marine biosphere during many periods of Earth’s history